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FinMath
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Learn the math of Introductory Finance in less than two weeks! Our App does not rely on static data, instead it uses a unique Artificial Intelligence (AI) approach to coach and create thousands of examples and applications for the student to master the concepts.

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Firm and Project Valuation

The final two chapters teach you how to value a firm or a project, given all the information about projected sales and the associated costs, given the initial investment toward plant and equipment, and the cost of capital. In evaluating these firms and projects, we come across numerous methods researchers, and practitioners use to assess them. We discuss the differences and similarities between these methods as we search for the best valuation method. We use solved examples and real-world exercises, even though we have to resort to spreadsheets instead of equations as the applications get more complicated. The process leads us to a paradigm that we continue to use right up to the final course in finance and industry.

Cost of Capital

Our ultimate objective is to learn how to value firms and projects that firms may wish to do. However, before we do that, we now realize that all cash flows are risky and may require different returns. We also know that firms raise money for their various projects by using a mixture of stocks and bonds. So, we need a way to access the cost of capital of the firm or project we wish to evaluate. In Chapters 7 and 8, we assess the cost of capital of various stakeholders (shareholders, bondholders, and others) and estimate their expected returns based on the risk they face. We find that the uncertainty assumed by each stakeholder results in a corresponding reward in expected return. However, the riskiness of the firm and its expected return remain unchanged. This critical finding leads to the famous M&M theorem of a firm. As usual, we try to ease your learning by using several solved examples, exercises with answers, and numerous real-world exercises.

Risk and Return

A question that most practitioners in finance either tend to ignore or forget to consider concerns the risk of the future, uncertain cash flows. You will want to get a higher return from cash flows that are riskier. For example, stock returns are more uncertain than bond returns and, therefore, given the same cash flows from the two, we should expect a higher return from stocks. In the first place, however, what is “return” and what is “risk?” How do we define these concepts mathematically, and how do we tie them together? More formally, how do we find a relationship between these two concepts? It turns out that by asking these questions, we discover numerous gems in the field of finance, such as the concept of diversification and the Capital Pricing Model (CAPM). These findings, among others, led several great researchers to win Nobel prizes in the field of financial economics.

Valuation of Bonds and Stocks

The following two chapters deal with investment and trading in bonds and stocks. Any time you want to buy shares of Tesla or Apple, how do you decide the right price to pay? The answer is not necessarily obvious or easy but certainly, be solved. The answers could differ for various reasons, for if we all agreed, there would be no trading! Bonds have relatively more straightforward cash flows, but that does not mean they are easier to value. Bond valuation tends to be more mathematical, and stocks require better gut instincts to appreciate.

Valuation of Cash Flows

Finance is deeply concerned with valuation. The generic question is how to assign a value today to a future set of uncertain cash flows. This question is so pervasive in our modern society. For example, if Jerry plans to lease a car with a monthly payment of $350 for 36 months, how much is he paying in today’s value? The first two chapters focus solely on valuing various types of cash flows; single cash flows, constant cash flows, growing or irregular cash flows, finite or infinite cash flows. We make this boring topic lively with the creative use of many real-life examples. Numerous solved examples and exercises with answers follow each section.